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Short Edge of Pentagonal Hexecontahedron given Midsphere Radius Formula

GoShort Edge of Pentagonal Hexecontahedron given Long Edge Formula

GoShort Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge Formula

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Short Edge of Pentagonal Hexecontahedron is the length of the shortest edge which is the base and middle edge of the axial-symmetric pentagonal faces of the Pentagonal Hexecontahedron. Check FAQs

l e(Short) = \frac{r m}{\sqrt{\frac{1 + 0.4715756}{2 \cdot (1 - 2 \cdot 0.4715756)}}}

l_e(Short) - Short Edge of Pentagonal Hexecontahedron?r_m - Midsphere Radius of Pentagonal Hexecontahedron?

Short Edge of Pentagonal Hexecontahedron given Midsphere Radius Example

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Here is how the Short Edge of Pentagonal Hexecontahedron given Midsphere Radius equation looks like with Values.

Here is how the Short Edge of Pentagonal Hexecontahedron given Midsphere Radius equation looks like with Units.

Here is how the Short Edge of Pentagonal Hexecontahedron given Midsphere Radius equation looks like.

4.1694 = \frac{15}{\sqrt{\frac{1 + 0.4715756}{2 \cdot (1 - 2 \cdot 0.4715756)}}}

4.1694m = \frac{15m}{\sqrt{\frac{1 + 0.4715756}{2 \cdot (1 - 2 \cdot 0.4715756)}}}

4.1694 = \frac{15}{\sqrt{\frac{1 + 0.4715756}{2 \cdot (1 - 2 \cdot 0.4715756)}}}

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Short Edge of Pentagonal Hexecontahedron given Midsphere Radius Solution

Follow our step by step solution on how to calculate Short Edge of Pentagonal Hexecontahedron given Midsphere Radius?

FIRST Step Consider the formula

l e(Short) = \frac{r m}{\sqrt{\frac{1 + 0.4715756}{2 \cdot (1 - 2 \cdot 0.4715756)}}}

Next Step Substitute values of Variables

∴

l e(Short) = \frac{15m}{\sqrt{\frac{1 + 0.4715756}{2 \cdot (1 - 2 \cdot 0.4715756)}}}

Next Step Prepare to Evaluate

∴

l e(Short) = \frac{15}{\sqrt{\frac{1 + 0.4715756}{2 \cdot (1 - 2 \cdot 0.4715756)}}}

Next Step Evaluate

∴

l e(Short) = 4.16941974408556m

LAST Step Rounding Answer

∴

l e(Short) = 4.1694m

Short Edge of Pentagonal Hexecontahedron given Midsphere Radius Formula Elements

Variables

Functions

Short Edge of Pentagonal Hexecontahedron

Short Edge of Pentagonal Hexecontahedron is the length of the shortest edge which is the base and middle edge of the axial-symmetric pentagonal faces of the Pentagonal Hexecontahedron.

Symbol: l_e(Short)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Short Edge of Pentagonal Hexecontahedron

Midsphere Radius of Pentagonal Hexecontahedron

Midsphere Radius of Pentagonal Hexecontahedron is the radius of the sphere for which all the edges of the Pentagonal Hexecontahedron become a tangent line on that sphere.

Symbol: r_m

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Midsphere Radius of Pentagonal Hexecontahedron

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Short Edge of Pentagonal Hexecontahedron

Go Short Edge of Pentagonal Hexecontahedron given Long Edge

l e(Short) = \frac{31 \cdot l e(Long)}{((7 \cdot [phi] + 2) + (5 \cdot [phi] - 3) + 2 \cdot (8 - 3 \cdot [phi])) \cdot \sqrt{2 + 2 \cdot (0.4715756)}}

Go Short Edge of Pentagonal Hexecontahedron given Snub Dodecahedron Edge

l e(Short) = \frac{l e(Snub Dodecahedron)}{\sqrt{2 + 2 \cdot (0.4715756)}}

Go Short Edge of Pentagonal Hexecontahedron given Total Surface Area

l e(Short) = \sqrt{\frac{TSA \cdot (1 - 2 \cdot {0.4715756}^{2})}{30 \cdot (2 + 3 \cdot 0.4715756) \cdot \sqrt{1 - {0.4715756}^{2}}}}

Go Short Edge of Pentagonal Hexecontahedron given Volume

l e(Short) = {(\frac{V \cdot (1 - 2 \cdot {0.4715756}^{2}) \cdot \sqrt{1 - 2 \cdot 0.4715756}}{5 \cdot (1 + 0.4715756) \cdot (2 + 3 \cdot 0.4715756)})}^{\frac{1}{3}}

How to Evaluate Short Edge of Pentagonal Hexecontahedron given Midsphere Radius?

Short Edge of Pentagonal Hexecontahedron given Midsphere Radius evaluator uses Short Edge of Pentagonal Hexecontahedron = Midsphere Radius of Pentagonal Hexecontahedron/sqrt((1+0.4715756)/(2*(1-2*0.4715756))) to evaluate the Short Edge of Pentagonal Hexecontahedron, Short Edge of Pentagonal Hexecontahedron given Midsphere Radius formula is defined as the length of shortest edge which is the base and middle edge of the axial-symmetric pentagonal faces of the Pentagonal Hexecontahedron, calculated using midsphere radius of Pentagonal Hexecontahedron. Short Edge of Pentagonal Hexecontahedron is denoted by l_e(Short) symbol.

How to evaluate Short Edge of Pentagonal Hexecontahedron given Midsphere Radius using this online evaluator? To use this online evaluator for Short Edge of Pentagonal Hexecontahedron given Midsphere Radius, enter Midsphere Radius of Pentagonal Hexecontahedron (r_m) and hit the calculate button.

FAQs on Short Edge of Pentagonal Hexecontahedron given Midsphere Radius

What is the formula to find Short Edge of Pentagonal Hexecontahedron given Midsphere Radius?

The formula of Short Edge of Pentagonal Hexecontahedron given Midsphere Radius is expressed as Short Edge of Pentagonal Hexecontahedron = Midsphere Radius of Pentagonal Hexecontahedron/sqrt((1+0.4715756)/(2*(1-2*0.4715756))). Here is an example- 4.16942 = 15/sqrt((1+0.4715756)/(2*(1-2*0.4715756))).

How to calculate Short Edge of Pentagonal Hexecontahedron given Midsphere Radius?

With Midsphere Radius of Pentagonal Hexecontahedron (r_m) we can find Short Edge of Pentagonal Hexecontahedron given Midsphere Radius using the formula - Short Edge of Pentagonal Hexecontahedron = Midsphere Radius of Pentagonal Hexecontahedron/sqrt((1+0.4715756)/(2*(1-2*0.4715756))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Short Edge of Pentagonal Hexecontahedron?

Here are the different ways to Calculate Short Edge of Pentagonal Hexecontahedron-

Short Edge of Pentagonal Hexecontahedron=(31*Long Edge of Pentagonal Hexecontahedron)/(((7*[phi]+2)+(5*[phi]-3)+2*(8-3*[phi]))*sqrt(2+2*(0.4715756)))
Short Edge of Pentagonal Hexecontahedron=Snub Dodecahedron Edge Pentagonal Hexecontahedron/sqrt(2+2*(0.4715756))
Short Edge of Pentagonal Hexecontahedron=sqrt((Total Surface Area of Pentagonal Hexecontahedron*(1-2*0.4715756^2))/(30*(2+3*0.4715756)*sqrt(1-0.4715756^2)))

Can the Short Edge of Pentagonal Hexecontahedron given Midsphere Radius be negative?

No, the Short Edge of Pentagonal Hexecontahedron given Midsphere Radius, measured in Length cannot be negative.

Which unit is used to measure Short Edge of Pentagonal Hexecontahedron given Midsphere Radius?

Short Edge of Pentagonal Hexecontahedron given Midsphere Radius is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Short Edge of Pentagonal Hexecontahedron given Midsphere Radius can be measured.

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